The injectivity radius of hyperbolic surfaces and some Morse functions over moduli spaces.
Event details
| Date | 25.11.2015 |
| Hour | 16:30 › 17:30 |
| Speaker | Matthieu Gendulphe (Roma) |
| Category | Conferences - Seminars |
Let X be a compact hyperbolic surface. The injectivity radius at a point p of X is the radius of the largest embedded metric ball centered at p, we denote it by R_p(X).
The extrema of the injectivity radius have been widely studied using different methods.
Schmutz and Bavard have developed a variational framework for the study of min_p R_p(X) as a function over the Teichmüller space.
Bavard and Deblois have used some geometric decompositions to bound max_p R_p(X) in terms of the topology of X.
In this talk I will present a variational approach for the study of the injectivity radius, seen as a function over the Teichmüller space of hyperbolic surfaces with a marked point.
I will show that this function is almost a Morse function, and I will determine all its critical points. As a consequence I will obtain some known inequalities due to Bavard and Deblois.
The extrema of the injectivity radius have been widely studied using different methods.
Schmutz and Bavard have developed a variational framework for the study of min_p R_p(X) as a function over the Teichmüller space.
Bavard and Deblois have used some geometric decompositions to bound max_p R_p(X) in terms of the topology of X.
In this talk I will present a variational approach for the study of the injectivity radius, seen as a function over the Teichmüller space of hyperbolic surfaces with a marked point.
I will show that this function is almost a Morse function, and I will determine all its critical points. As a consequence I will obtain some known inequalities due to Bavard and Deblois.
Practical information
- Informed public
- Free
Organizer
- Louis Merlin
Contact
- Louis Merlin